ISTANBUL, Turkey—Serena Williams has looked just about unbeatable since Wimbledon, with only one player, world No. 2 Victoria Azarenka, able to play her tough each time they face off. Williams has been pretty healthy since January, and when she’s feeling spry and is able to play freely, she has more weapons than anyone on tour.

But an exhausted or injured 32-year-old Williams is vulnerable, just like the tennis world saw back in January at Australian Open, when she injured her ankle and was eventually run out of the tournament by Sloane Stephens.

Coming into her semifinal against Jelena Jankovic at the WTA Championships, Williams had not lost a match since she went down to Azarenka in the final of Cincinnati. She had won the U.S. Open and Beijing, and none of the three players in her round-robin group came close to touching her earlier in this week in Istanbul.

But when the first set began against Jankovic, it was clear that Serena was physically in trouble. It appeared she had a back injury, because she was merely nudging her vaunted serve in. But it was not: Her long season had taken a toll on her and had engine had run dry. As she later said, she was on “E.”

Serena appeared to cry twice into her towel twice during changeovers, and was moving rather stiffly, when she was moving at all. Take away her serve—unquestionably the best in history—her lateral movement, and her bountiful confidence, and Jankovic had a very vulnerable 17-time Grand Slam champion on a silver platter.

But like a new waitress on her first night on the job, Jankovic dropped the platter, and her hopes of reaching the final went crashing to the floor.

Even though the Serbian had beaten Williams on four occasions entering this contest, there are reasons why Serena owned a 7-4 head-to-head record against her entering the semifinals and had won their last three matches: She’s mentally tougher by a wide margin, her forehand is far superior, and she is a much more competent match manager.

So even though Serena went down 3-1 in the first set and her exhaustion was obvious on her ultra-expressive face, she was more resourceful at crunch time.

It wasn't until the end of the first set that Serena lost a good 30 percent of her normal service speed. Somehow she managed to serve the first set out, but not before her legs began to feel rubbery; she tried an absurd drop shot that handed Jankovic a break point, which Serena managed to fend off with a cross-court forehand winner. On her third set point, Williams hammered a forehand cross-court that induced an error from Jankovic’s weaker forehand side.

Serena appeared relieved, but then her body want into a near coma in the second set. Jankovic began move the ball adeptly around and kept her shots deep; there were times that Serena didn't even try and run for balls that on a normal day would be well with her in range. She soft-balled serves down the middle, dumped forehands into net and pushed her return of serves.

The second set was gone in a flash of JJ’s Chesire cat smile.

As Serena’s coach Patrick Mouratoglou would later say, the third set was all about Serena understanding what she could and could not do. Yes, Williams is a warrior, but fighting hard doesn't get a player through every match, and in this one Serena had to use her junior toolbox rather than that of a master craftsman. So she decided to play steady until she got a clean look at openings, and for the most part she worked the lines beautifully.

Certainly, it was not easy for Jankovic to go up against a player who appeared to be injured, because she didn't know which strategy to employ. She seemed a little lost.

The two traded breaks to open the third set, then Serena broke Jankovic again to 2-1 with a big cross-court backhand. A few moments later and number of errors later, Jankovic found herself down 5-1. By that point, Serena was more energetic. It took a big effort for Jankovic to scratch back to 5-4, which she did by fighting off a match point.

Williams did not close out the match in her typical ferocious fashion, but she did enough to cross the line. Facing a break point, she kicked an ace on the line. At deuce she ripped an inside-out forehand winner, and then on her fourth match point, she hit a crisp approach shot and followed it up with a booming overhead.

Williams looked more relieved than thrilled and said that she would like to sleep for 24 hours. She can’t, as her final against Li Na is scheduled about 21 hours after her win of Jankovic concluded. This will be a great opportunity for the soon-to-be world No. 3 Li to get over on Serena for a big title, but even if Williams arrives on court on a stretcher, Li must be aware that even a broken-down Serena is still a very dangerous player.